If f (x) varies directly with x2, and f (x) = 40 when x = 2, find the value of f (6). 36 60 120 360

The answer is 360.

f (x) varies directly with x^2 and f (2) = 40. What does that mean?

It means this f (x) = k * x^2. We need to find k.

For x=2, f (x) = 40, this means k * x^2 = 40. BUT, x=2.

This means p * 2^2 = 40. = > k = 40 / 4 = 10.

We just found what f (x) is: f (x) = 10x^2.

Now, what is the value of f (6) ?

Just replace the value of k by 10. = > f (6) = 10 * 6^2 = 10*36 = 360